Multiple small glitches when beveling complex meshes
The glitches are caused by overlapping vertices. The only solution is proper topology, supporting the bevel.

If we examine the effect of the bevel modifier on your topology, we can see the vertices are badly positioned and the bevel quickly creates overlapping faces.



Position your edges parallel to each other and assert that the edges have a minimum length.
(In your file I had to apply previous modifiers.)



When you enable the Clamp option in the bevel modifier, the bevel modifier will determine how much it can bevel before vertices/edges overlap. However, if there are dense parts in your mesh this value will be very small and result in a tiny amount of bevel. This question shows that a solution would be to split the mesh into different parts, or use bevel weights in that case.



If you model geometry, especially using n-gons, be wary of the spacing of the edges and the topology. If you add a support loop (simply inset and scale), the first bevel modifier will work fine.